The source said ‘their baby girl was very early, it was a surprise to them both.’
Peter and Emily were staying in the Somerset countryside, hundreds of miles from his home in Surrey, when Emily went into labour.
Emily delivered their baby daughter three weeks early after her and Pete rushed to NHS Musgrove Park hospital.
Coincidentally, the hospital is reportedly the same place where Pete first met Emily’s surgeon father when he was admitted suffering from kidney stones.
Pete and Emily are still to reveal the name of their newborn but have hinted that they plan to choose a more traditional name.
Pete told a UK gossip magazine that he and Emily are taking their time to name their daughter.
He said:
"Thankyou to everyone for their kind messages on the arrival of our little beaut. She is just perfect."
"It's a bit early to say who she looks like yet, but I'm sure it will be apparent soon! Emily and baby are doing well. We have the next couple of weeks to think of a name."
"Our baby is girl is absolutely gorgeous. We're so happy. Although Ems was three weeks early, everything went to plan."
The couple’s new arrival is Pete’s third child. He has a son, Junior, and daughter, Princess, from his marriage with glamour model Katie Price.